Jianzhong Pan

activity

19992026

collaborators

6 papers

math.AT2026

Stable Cohomotopy in Codimensions Two and Three: From Algebraic Characterizations to Bordism-Theoretic Interpretations

Pengcheng Li, Jianzhong Pan, Jie Wu

This paper investigates stable cohomotopy groups in codimensions two and three from complementary algebraic and geometric viewpoints. For general CW complexes, we give a complete c…

math.AT2025

Homotopy classification of $S^{2 k - 1}$ -bundles over $S^{2 k}$

Zhongjian Zhu, Jianzhong Pan

In this paper, we classify the homotopy types of the total spaces of $S^{2 k - 1}$ -bundles (or fibrations) over $S^{2 k}$ for $2 \leq k \leq 6$ . One of the two key new ingredients in the…

math.AT2025

Complexes equivalent to $S^{2 k - 1}$ -fibrations over $S^{2 k}$

Zhongjian Zhu, Jianzhong Pan

In this paper, necessary and sufficient conditions are obtained for the attaching map $f$ of the top cell of a CW complex to have the homotopy type of the total space of $S^{2 k - 1}$ …

math.AT2023

2-local unstable homotopy groups of indecomposable $A_{3}^{2}$ -complexes

Zhongjian Zhu, Jianzhong Pan

In this paper, we calculate the 2-local unstable homotopy groups of indecomposable $A_{3}^{2}$ -complexes. The main technique used is analysing the homotopy property of $J(X,A)…

math.AT2001

Rational homotopy theory and nonnegative curvature

Jianzhong Pan

In this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that t…

math.AT1999

Forgetable map and phantom maps

Pan Jianzhong, Woo Moo Ha

In this note, we attack a question posed ten years ago by Tsukiyama about the injectivity of the so- called Forgetable map. We show that we can insert the Forgetable map in an exac…

Stable Cohomotopy in Codimensions Two and Three: From Algebraic Characterizations to Bordism-Theoretic Interpretations

Homotopy classification of S2k−1-bundles over S2k

Complexes equivalent to S2k−1-fibrations over S2k

2-local unstable homotopy groups of indecomposable A32​ -complexes

Rational homotopy theory and nonnegative curvature

Forgetable map and phantom maps

Homotopy classification of $S^{2 k - 1}$ -bundles over $S^{2 k}$

Complexes equivalent to $S^{2 k - 1}$ -fibrations over $S^{2 k}$

2-local unstable homotopy groups of indecomposable $A_{3}^{2}$ -complexes